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The present invention is related to numerical processing and more particularly to a method and computer-based apparatus involving the use of a new fundamental architecture using look-up tables for particularly efficient generation of general-purpose mathematical transformations (i.e., mappings) of numerical data. In particular, highly efficient general-purpose exponential and logarithmic generators are provided.
Prior art general-purpose logarithmic operations, compared with additions and subtractions and multiplications, have been inefficient and expensive--so much so that the inefficiency and expense are widely regarded as inevitable penalties on the logarithmic operation itself. For example, a commercial conventional numerical processor might execute logarithmic operations ten to twenty times slower than even its comparatively expensive multiply operation.
The present invention targets problems which have been thought unsolvable, problems which have not been recognized as problems, and problems which are major obstacles to practical implementation of general function generators. Major problems not recognized as such in the prior art include areas of analysis, notation, and terminology associated with such commonly used functions as the elementary exponentials and logarithms. These areas need to be extended in a number of distinctly fundamental directions.